A mathematical treatment of edge in characteristic non-reflecting boundary conditions is developed.Several numerical simulations show that this method is benefit for treating of waves.A spatially evolving compressible round jet is simulated with direct numerical simulation method.Simulation results are compared with experiments.It suggests that the method on edge boundary conditions is convincible.

A method is presented to deal with high-dimensional scalar PDF(probability density function) transport equation for two-phase flow in phase space (X, V), in which the PDF transport equation is reduced to velocity phase space.The particle velocity PDF f^v(V) is solved analytically and the particle position PDF is obtained statistically with Monte Carlo techniques. It shows that the method is better than the particle Reynolds stress trajectory model(PRST Model) in simulating a turbulent wall jet loaded with solid particles.